A control device for a vehicle power transmission device is conventionally known that executes a shift of a stepped automatic transmission disposed between an engine and a drive wheel based on a predetermined shift map (shift line diagram). For example, one example is a control device for a vehicle power transmission device described in Patent Document 1. The control device for a vehicle power transmission device of Patent Document 1 has two types of running modes, which are a normal running mode and a fuel consumption saving running mode of running with an engine rotation speed suppressed as compared to the normal running mode. The control device stores a shift map for the normal running mode and a shift map for the fuel consumption saving running mode in advance so as to realize the two types of running modes. In either of the shift maps, a vehicle speed and an accelerator opening degree are used as parameters, i.e., a shift point of the automatic transmission is set by the vehicle speed and the accelerator opening degree.